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平面上的三点共线与空间的四点共面,是平面向量与空间向量问题中的一类重要题型。在高中数学人教A版选修教材2-1《空间向量与立体几何》一章中,给出了四点共面的一个判定方法,在配套的教参中更明确为充要条件。因此有些老师在教学中就给出了如下的空间P、A、B、C、四点共面的充要条件:对于空间任意一点O,存在实数x、y、z,使得且x+y+z=1。这个结论对于解决空间四点共面问题提供了很便捷的方法。
Plane three-point collinear and space four-point coplanarity, plane vector and space vector problem is an important type of questions. In high school mathematics teaching A version of elective textbook 2-1 “space vector and the three-dimensional geometry” chapter, gives a four-point coplanarity of a decision method, in the teaching parameters more explicit as a necessary and sufficient condition. Therefore, some teachers give the following necessary and sufficient conditions for four-point coplanar P, A, B, C in teaching: For any point O in space, there are real numbers x, y, z such that x + y + z = 1. This conclusion provides a very convenient way to solve the four-point coplanar problem in space.